An important object of seismic reflection is to produce a seismic section which corresponds as closely as possible to an image of the elastic reflectivity of the subsurface region which is being explored.
The elastic reflectivity of a subsurface region can be used either to spatially reposition the geometry of the seismic reflectors or horizons, that is to say events which have spatial continuity and which are characteristic of significant geological events, in which case information is then obtained regarding the structure of the subsurface region being explored, or to quantitatively measure the reflectivity or the reflection coefficient, in which case information is then obtained, on the one hand regarding the petroelastic parameter contrasts of a given geological event and, on the other hand regarding the quality of the rocks which caused the reflectivity which is measured.
By applying a variety of theories, for example diffracting point theories, it has become possible to produce seismic images which give a better representation of the reflectivity of the subsurface region being explored.
One of the most widespread methods consists, in particular, in recording seismic traces from the subsurface region. These traces are sorted according to a given criterion, for example common shotpoint, common offset, common midpoint, etc. to obtain one or more trace collections sorted according to the chosen criterion. Then, time or depth-migrating the trace collection or collections previously sorted, using a velocity model which may or may not be defined beforehand but which relates to a zone of the subsurface region, the migration being, for example, of the Kirchhoff type.
All the migration methods are based implicitly or explicitly on stacks (integrals) and are well known to those skilled in the art. The methods based implicitly on stacks are, for example, the methods referred to as wave equation methods, while the methods resorting explicitly to stacks are, for example, the migration methods referred to as Kirchhoff, Born inversion or other migration methods equivalent to these. Each trace of the migrated collection may or may not be weighted, depending on the desired object.
When the object is to obtain, quickly and with low processing costs, an image of the subsurface region which is sufficient for so-called structural interpretation, it is possible either not to use weights (unweighted process) or to use weights which are very rough approximations. However, a technique of this type cannot be used in a much more refined analysis of the amplitude versus offset (AVO) type.
When the desire is, for example, to carry out preserved amplitude migration, it is then essential to weight the traces with suitable weights. Reference may usefully be made to the article by Tygel, published in Geophysics, vol. 59, No. 12 of December 1993, which is a good survey of the techniques employed and which describes the stationary phase theory.
The weighting given to each trace is referred to as the "Green function" and essentially comprises two terms:
(a) transit times, which are needed irrespective of the migration method used, and PA1 (b) weights which are calculated accurately and applied to each sample used in Kirchhoff stacking, for example.
This therefore makes it necessary to calculate a very large number of weights, equal to the number of samples involved in the migration, and this is relatively very expensive. Proper processing, that is to say calculating the weights, occupies a computer for several days.